## Rachel98 2 years ago I don't really get this. Question: Use the rules for exponents and roots to prove that 512^2/3 = 16^3/2

1. mjr632

Do you mean a rigorous formal proof?

2. Rachel98

I don't really know. This is what the question was and I don't get it.

3. mjr632

Do you understand how to use logarithms?

4. Rachel98

No

5. mjr632

Ah, you will want to understand natural logarithms for this question, I can explain it.

6. mjr632

$y = \log_b x$ $x = b^y$

7. mjr632

If we take the natural logarithm of $512^{\frac{2}{3}}$ $\frac{2}{3}\ln(512)$

8. mjr632

We can pull the exponent out

9. Rachel98

So, is that a cube root? That we ended up with?

10. precal

|dw:1360950294527:dw|

11. precal

|dw:1360950347726:dw|

12. precal

|dw:1360950360574:dw|

13. precal

|dw:1360950390774:dw|

14. precal

|dw:1360950432326:dw|

15. precal

yes they are both equivalent

16. Rachel98

Thanks, so much. That makes sense now.

17. precal

yw

18. precal

no need to use logs here

19. ghass1978

just using exponents :512=2^9 so 512^(2/3)=2^6 and 16^(3/2)=2^6 so both are equal

20. Rachel98

Thanks

21. precal

yw